Professor S. gives two assignments in her class. She uses the higher of the two grades when she wants to calculate the final grade for the course
(a) Suppose x1 represents the grade for assignment 1 and x2 shows the grade for assignment 2. Alice wants to maximize her grade. On a graph draw an indifference curve showing all the combinations that Alice likes as much as x1 = 80 and x2 = 40. Draw another indifference curve showing all the combinations that Alice likes as much as x1 = 70 and x2 = 70.
(b) Does Alice have convex preferences over these combinations?
(c) Observing that students do not study hard, Professor S. changes her policy to using the lower of the two grades to calculate the course grade. With a different color, draw an indifference curve showing all the combinations that Alice likes as much as x1 = 80 and x2 = 40. Draw another indifference curve showing all the combinations that Alice likes as much as x1 = 70 and x2 = 70.
(d) Does Alice have convex preferences over these combinations?